Math
Vector operations.
Definition
Vector operations include adding, subtracting, and scaling vectors, as well as computing the dot product. Vectors are quantities that have both magnitude (size) and direction, and these operations follow specific rules different from regular number arithmetic.
Examples
Real-world.
- 1 Adding vectors: ⟨2, 3⟩ + ⟨4, 1⟩ = ⟨6, 4⟩
- 2 Scalar multiplication: 3⟨2, −1⟩ = ⟨6, −3⟩
- 3 Finding the magnitude of ⟨3, 4⟩: √(9 + 16) = 5
Key Fact
Magnitude of vector ⟨a, b⟩ = √(a² + b²)